%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL140-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:49:08 AM UTC 2026
% Result : Unsatisfiable 0.21s 0.54s
% Output : CNFRefutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 68
% Number of leaves : 5
% Syntax : Number of clauses : 174 ( 174 unt; 0 nHn; 59 RR)
% Number of literals : 174 ( 173 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 142 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
not(not(x)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_lemma) ).
cnf(c2,axiom,
implies(truth,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_1) ).
cnf(c3,plain,
implies(truth,not(not(X2))) = not(not(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
not(not(X2)) = implies(truth,not(not(X2))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
implies(truth,implies(not(truth),X2)) = implies(not(truth),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
implies(not(truth),X2) = implies(truth,implies(not(truth),X2)),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c8,plain,
implies(X2,X2) = implies(implies(truth,X2),X2),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
implies(truth,implies(implies(truth,X2),X2)) = implies(implies(truth,X2),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
implies(implies(truth,X2),X2) = implies(truth,implies(implies(truth,X2),X2)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c12,plain,
implies(implies(X3,X2),X2) = implies(implies(X3,X2),implies(truth,X2)),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
implies(X3,implies(implies(X3,X2),X2)) = implies(X3,implies(implies(X3,X2),implies(truth,X2))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c15,plain,
implies(X3,implies(implies(X3,X2),implies(truth,X2))) = implies(implies(truth,X3),implies(implies(X3,X2),implies(truth,X2))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,axiom,
implies(implies(X2,Y),implies(implies(Y,Z),implies(X2,Z))) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_2) ).
cnf(c17,plain,
implies(implies(truth,X3),implies(implies(X3,X2),implies(truth,X2))) = truth,
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
implies(X3,implies(implies(X3,X2),implies(truth,X2))) = truth,
inference(transitivity,[status(thm)],[c15,c17]) ).
cnf(c19,plain,
implies(X3,implies(implies(X3,X2),X2)) = truth,
inference(transitivity,[status(thm)],[c13,c18]) ).
cnf(c20,plain,
implies(truth,implies(implies(truth,X2),X2)) = truth,
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
implies(implies(truth,X2),X2) = truth,
inference(transitivity,[status(thm)],[c10,c20]) ).
cnf(c22,plain,
implies(X2,X2) = truth,
inference(transitivity,[status(thm)],[c8,c21]) ).
cnf(c23,plain,
truth = implies(X2,X2),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
implies(X2,truth) = implies(X2,implies(X2,X2)),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,axiom,
implies(implies(X2,Y2),Y2) = implies(implies(Y2,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_3) ).
cnf(c26,plain,
implies(implies(truth,X2),X2) = implies(implies(X2,truth),truth),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
implies(implies(X2,truth),truth) = implies(implies(truth,X2),X2),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
implies(implies(truth,X2),X2) = implies(X2,X2),
inference(congruence,[status(thm)],[c2]) ).
cnf(c29,plain,
implies(implies(X2,truth),truth) = implies(X2,X2),
inference(transitivity,[status(thm)],[c27,c28]) ).
cnf(c30,plain,
implies(X2,X2) = implies(implies(X2,truth),truth),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
implies(X2,implies(X2,X2)) = implies(X2,implies(implies(X2,truth),truth)),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
implies(X2,implies(implies(X2,truth),truth)) = truth,
inference(substitution,[status(thm)],[c19]) ).
cnf(c33,plain,
implies(X2,implies(X2,X2)) = truth,
inference(transitivity,[status(thm)],[c31,c32]) ).
cnf(c34,plain,
implies(X2,truth) = truth,
inference(transitivity,[status(thm)],[c24,c33]) ).
cnf(c35,plain,
implies(not(X2),truth) = truth,
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
truth = implies(not(X2),truth),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
implies(truth,implies(not(truth),X2)) = implies(implies(not(X2),truth),implies(not(truth),X2)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
implies(truth,not(not(truth))) = not(not(truth)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c39,plain,
not(not(truth)) = implies(truth,not(not(truth))),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
implies(truth,implies(truth,not(not(truth)))) = implies(truth,not(not(truth))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c41,plain,
implies(truth,not(not(truth))) = implies(truth,implies(truth,not(not(truth)))),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
implies(implies(X2,X3),X3) = implies(implies(X3,X2),X2),
inference(substitution,[status(thm)],[c25]) ).
cnf(c43,plain,
implies(implies(X3,X2),X2) = implies(implies(X2,X3),X3),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
implies(implies(implies(X3,X2),X2),X3) = implies(implies(implies(X2,X3),X3),X3),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
implies(implies(implies(X2,X3),X3),X3) = implies(implies(X3,implies(X2,X3)),implies(X2,X3)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c46,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c47,plain,
implies(X3,implies(X2,X3)) = implies(implies(truth,X3),implies(X2,X3)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
implies(truth,implies(implies(truth,X3),implies(X2,X3))) = implies(implies(truth,X3),implies(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c49,plain,
implies(implies(truth,X3),implies(X2,X3)) = implies(truth,implies(implies(truth,X3),implies(X2,X3))),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
truth = implies(X2,truth),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c51,plain,
implies(truth,implies(implies(truth,X3),implies(X2,X3))) = implies(implies(X2,truth),implies(implies(truth,X3),implies(X2,X3))),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
implies(implies(X2,truth),implies(implies(truth,X3),implies(X2,X3))) = truth,
inference(substitution,[status(thm)],[c16]) ).
cnf(c53,plain,
implies(truth,implies(implies(truth,X3),implies(X2,X3))) = truth,
inference(transitivity,[status(thm)],[c51,c52]) ).
cnf(c54,plain,
implies(implies(truth,X3),implies(X2,X3)) = truth,
inference(transitivity,[status(thm)],[c49,c53]) ).
cnf(c55,plain,
implies(X3,implies(X2,X3)) = truth,
inference(transitivity,[status(thm)],[c47,c54]) ).
cnf(c56,plain,
implies(implies(X3,implies(X2,X3)),implies(X2,X3)) = implies(truth,implies(X2,X3)),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
implies(truth,implies(X2,X3)) = implies(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c58,plain,
implies(implies(X3,implies(X2,X3)),implies(X2,X3)) = implies(X2,X3),
inference(transitivity,[status(thm)],[c56,c57]) ).
cnf(c59,plain,
implies(implies(implies(X2,X3),X3),X3) = implies(X2,X3),
inference(transitivity,[status(thm)],[c45,c58]) ).
cnf(c60,plain,
implies(implies(implies(X3,X2),X2),X3) = implies(X2,X3),
inference(transitivity,[status(thm)],[c44,c59]) ).
cnf(c61,plain,
implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(truth)) = implies(not(not(truth)),not(truth)),
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
implies(not(not(truth)),not(truth)) = implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(truth)),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth))) = implies(not(truth),not(not(truth))),
inference(substitution,[status(thm)],[c60]) ).
cnf(c64,plain,
implies(not(truth),not(not(truth))) = implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth))),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c66,plain,
implies(implies(not(X2),not(truth)),X2) = implies(implies(not(X2),not(truth)),implies(truth,X2)),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,axiom,
implies(implies(not(X2),not(Y2)),implies(Y2,X2)) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_4) ).
cnf(c68,plain,
implies(implies(not(X2),not(truth)),implies(truth,X2)) = truth,
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
implies(implies(not(X2),not(truth)),X2) = truth,
inference(transitivity,[status(thm)],[c66,c68]) ).
cnf(c70,plain,
implies(implies(not(not(truth)),not(truth)),not(truth)) = truth,
inference(substitution,[status(thm)],[c69]) ).
cnf(c71,plain,
implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth))) = implies(truth,not(not(truth))),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
implies(truth,not(not(truth))) = not(not(truth)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c73,plain,
implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth))) = not(not(truth)),
inference(transitivity,[status(thm)],[c71,c72]) ).
cnf(c74,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference(transitivity,[status(thm)],[c64,c73]) ).
cnf(c75,plain,
implies(implies(not(truth),not(not(truth))),not(not(truth))) = implies(not(not(truth)),not(not(truth))),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(truth)) = implies(implies(not(not(truth)),not(not(truth))),not(truth)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
implies(not(not(truth)),not(not(truth))) = truth,
inference(substitution,[status(thm)],[c22]) ).
cnf(c78,plain,
implies(implies(not(not(truth)),not(not(truth))),not(truth)) = implies(truth,not(truth)),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
implies(truth,not(truth)) = not(truth),
inference(substitution,[status(thm)],[c2]) ).
cnf(c80,plain,
implies(implies(not(not(truth)),not(not(truth))),not(truth)) = not(truth),
inference(transitivity,[status(thm)],[c78,c79]) ).
cnf(c81,plain,
implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(truth)) = not(truth),
inference(transitivity,[status(thm)],[c76,c80]) ).
cnf(c82,plain,
implies(not(not(truth)),not(truth)) = not(truth),
inference(transitivity,[status(thm)],[c62,c81]) ).
cnf(c83,plain,
not(truth) = implies(not(not(truth)),not(truth)),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
implies(not(not(not(truth))),not(truth)) = implies(not(not(not(truth))),implies(not(not(truth)),not(truth))),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
implies(truth,implies(not(not(truth)),not(not(not(truth))))) = implies(not(not(truth)),not(not(not(truth)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c86,plain,
implies(not(not(truth)),not(not(not(truth)))) = implies(truth,implies(not(not(truth)),not(not(not(truth))))),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
implies(not(not(not(truth))),implies(not(not(truth)),not(not(not(truth))))) = truth,
inference(substitution,[status(thm)],[c55]) ).
cnf(c88,plain,
truth = implies(not(not(not(truth))),implies(not(not(truth)),not(not(not(truth))))),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
implies(truth,implies(not(not(truth)),not(not(not(truth))))) = implies(implies(not(not(not(truth))),implies(not(not(truth)),not(not(not(truth))))),implies(not(not(truth)),not(not(not(truth))))),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
implies(implies(implies(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) = implies(implies(not(not(not(truth))),implies(not(not(truth)),not(not(not(truth))))),implies(not(not(truth)),not(not(not(truth))))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c91,plain,
implies(implies(not(not(not(truth))),implies(not(not(truth)),not(not(not(truth))))),implies(not(not(truth)),not(not(not(truth))))) = implies(implies(implies(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c92,plain,
implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = implies(implies(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c93,plain,
implies(implies(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))) = implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
not(not(truth)) = implies(not(truth),not(not(truth))),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c95,plain,
implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = implies(implies(not(not(not(truth))),not(not(truth))),implies(not(truth),not(not(truth)))),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
implies(implies(not(not(not(truth))),not(not(truth))),implies(not(truth),not(not(truth)))) = truth,
inference(substitution,[status(thm)],[c67]) ).
cnf(c97,plain,
implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = truth,
inference(transitivity,[status(thm)],[c95,c96]) ).
cnf(c98,plain,
implies(implies(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))) = truth,
inference(transitivity,[status(thm)],[c93,c97]) ).
cnf(c99,plain,
implies(implies(implies(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) = implies(truth,not(not(not(truth)))),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
implies(truth,not(not(not(truth)))) = not(not(not(truth))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c101,plain,
implies(implies(implies(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) = not(not(not(truth))),
inference(transitivity,[status(thm)],[c99,c100]) ).
cnf(c102,plain,
implies(implies(not(not(not(truth))),implies(not(not(truth)),not(not(not(truth))))),implies(not(not(truth)),not(not(not(truth))))) = not(not(not(truth))),
inference(transitivity,[status(thm)],[c91,c101]) ).
cnf(c103,plain,
implies(truth,implies(not(not(truth)),not(not(not(truth))))) = not(not(not(truth))),
inference(transitivity,[status(thm)],[c89,c102]) ).
cnf(c104,plain,
implies(not(not(truth)),not(not(not(truth)))) = not(not(not(truth))),
inference(transitivity,[status(thm)],[c86,c103]) ).
cnf(c105,plain,
not(not(not(truth))) = implies(not(not(truth)),not(not(not(truth)))),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
implies(not(not(not(truth))),implies(not(not(truth)),not(truth))) = implies(implies(not(not(truth)),not(not(not(truth)))),implies(not(not(truth)),not(truth))),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
implies(implies(not(not(truth)),not(not(not(truth)))),implies(not(not(truth)),not(truth))) = truth,
inference(substitution,[status(thm)],[c67]) ).
cnf(c108,plain,
implies(not(not(not(truth))),implies(not(not(truth)),not(truth))) = truth,
inference(transitivity,[status(thm)],[c106,c107]) ).
cnf(c109,plain,
implies(not(not(not(truth))),not(truth)) = truth,
inference(transitivity,[status(thm)],[c84,c108]) ).
cnf(c110,plain,
truth = implies(not(not(not(truth))),not(truth)),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
implies(truth,implies(truth,not(not(truth)))) = implies(implies(not(not(not(truth))),not(truth)),implies(truth,not(not(truth)))),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
implies(implies(not(not(not(truth))),not(truth)),implies(truth,not(not(truth)))) = truth,
inference(substitution,[status(thm)],[c67]) ).
cnf(c113,plain,
implies(truth,implies(truth,not(not(truth)))) = truth,
inference(transitivity,[status(thm)],[c111,c112]) ).
cnf(c114,plain,
implies(truth,not(not(truth))) = truth,
inference(transitivity,[status(thm)],[c41,c113]) ).
cnf(c115,plain,
not(not(truth)) = truth,
inference(transitivity,[status(thm)],[c39,c114]) ).
cnf(c116,plain,
truth = not(not(truth)),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
implies(not(X2),truth) = implies(not(X2),not(not(truth))),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
implies(implies(not(X2),truth),implies(not(truth),X2)) = implies(implies(not(X2),not(not(truth))),implies(not(truth),X2)),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
implies(implies(not(X2),not(not(truth))),implies(not(truth),X2)) = truth,
inference(substitution,[status(thm)],[c67]) ).
cnf(c120,plain,
implies(implies(not(X2),truth),implies(not(truth),X2)) = truth,
inference(transitivity,[status(thm)],[c118,c119]) ).
cnf(c121,plain,
implies(truth,implies(not(truth),X2)) = truth,
inference(transitivity,[status(thm)],[c37,c120]) ).
cnf(c122,plain,
implies(not(truth),X2) = truth,
inference(transitivity,[status(thm)],[c6,c121]) ).
cnf(c123,plain,
implies(not(truth),not(not(X2))) = truth,
inference(substitution,[status(thm)],[c122]) ).
cnf(c124,plain,
truth = implies(not(truth),not(not(X2))),
inference(symmetry,[status(thm)],[c123]) ).
cnf(c125,plain,
implies(truth,not(not(X2))) = implies(implies(not(truth),not(not(X2))),not(not(X2))),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
implies(implies(not(not(X2)),not(truth)),not(truth)) = implies(implies(not(truth),not(not(X2))),not(not(X2))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c127,plain,
implies(implies(not(truth),not(not(X2))),not(not(X2))) = implies(implies(not(not(X2)),not(truth)),not(truth)),
inference(symmetry,[status(thm)],[c126]) ).
cnf(c128,plain,
implies(truth,implies(not(X2),not(truth))) = implies(not(X2),not(truth)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c129,plain,
implies(not(X2),not(truth)) = implies(truth,implies(not(X2),not(truth))),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
implies(truth,implies(X2,implies(not(X2),not(truth)))) = implies(X2,implies(not(X2),not(truth))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c131,plain,
implies(X2,implies(not(X2),not(truth))) = implies(truth,implies(X2,implies(not(X2),not(truth)))),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c132,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c133,plain,
implies(not(implies(X2,not(truth))),X2) = implies(not(implies(X2,not(truth))),implies(truth,X2)),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
truth = implies(not(truth),X2),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c135,plain,
implies(truth,X2) = implies(implies(not(truth),X2),X2),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
implies(not(implies(X2,not(truth))),implies(truth,X2)) = implies(not(implies(X2,not(truth))),implies(implies(not(truth),X2),X2)),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
implies(implies(X2,not(truth)),not(truth)) = implies(implies(not(truth),X2),X2),
inference(substitution,[status(thm)],[c25]) ).
cnf(c138,plain,
implies(implies(not(truth),X2),X2) = implies(implies(X2,not(truth)),not(truth)),
inference(symmetry,[status(thm)],[c137]) ).
cnf(c139,plain,
implies(not(implies(X2,not(truth))),implies(implies(not(truth),X2),X2)) = implies(not(implies(X2,not(truth))),implies(implies(X2,not(truth)),not(truth))),
inference(congruence,[status(thm)],[c138]) ).
cnf(c140,plain,
implies(truth,not(X2)) = not(X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c141,plain,
not(X2) = implies(truth,not(X2)),
inference(symmetry,[status(thm)],[c140]) ).
cnf(c142,plain,
implies(not(X2),implies(X2,not(truth))) = implies(implies(truth,not(X2)),implies(X2,not(truth))),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
truth = not(not(truth)),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c144,plain,
implies(truth,not(X2)) = implies(not(not(truth)),not(X2)),
inference(congruence,[status(thm)],[c143]) ).
cnf(c145,plain,
implies(implies(truth,not(X2)),implies(X2,not(truth))) = implies(implies(not(not(truth)),not(X2)),implies(X2,not(truth))),
inference(congruence,[status(thm)],[c144]) ).
cnf(c146,plain,
implies(implies(not(not(truth)),not(X2)),implies(X2,not(truth))) = truth,
inference(substitution,[status(thm)],[c67]) ).
cnf(c147,plain,
implies(implies(truth,not(X2)),implies(X2,not(truth))) = truth,
inference(transitivity,[status(thm)],[c145,c146]) ).
cnf(c148,plain,
implies(not(X2),implies(X2,not(truth))) = truth,
inference(transitivity,[status(thm)],[c142,c147]) ).
cnf(c149,plain,
implies(not(implies(X2,not(truth))),implies(implies(X2,not(truth)),not(truth))) = truth,
inference(substitution,[status(thm)],[c148]) ).
cnf(c150,plain,
implies(not(implies(X2,not(truth))),implies(implies(not(truth),X2),X2)) = truth,
inference(transitivity,[status(thm)],[c139,c149]) ).
cnf(c151,plain,
implies(not(implies(X2,not(truth))),implies(truth,X2)) = truth,
inference(transitivity,[status(thm)],[c136,c150]) ).
cnf(c152,plain,
implies(not(implies(X2,not(truth))),X2) = truth,
inference(transitivity,[status(thm)],[c133,c151]) ).
cnf(c153,plain,
implies(not(implies(not(X2),not(truth))),not(X2)) = truth,
inference(substitution,[status(thm)],[c152]) ).
cnf(c154,plain,
truth = implies(not(implies(not(X2),not(truth))),not(X2)),
inference(symmetry,[status(thm)],[c153]) ).
cnf(c155,plain,
implies(truth,implies(X2,implies(not(X2),not(truth)))) = implies(implies(not(implies(not(X2),not(truth))),not(X2)),implies(X2,implies(not(X2),not(truth)))),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
implies(implies(not(implies(not(X2),not(truth))),not(X2)),implies(X2,implies(not(X2),not(truth)))) = truth,
inference(substitution,[status(thm)],[c67]) ).
cnf(c157,plain,
implies(truth,implies(X2,implies(not(X2),not(truth)))) = truth,
inference(transitivity,[status(thm)],[c155,c156]) ).
cnf(c158,plain,
implies(X2,implies(not(X2),not(truth))) = truth,
inference(transitivity,[status(thm)],[c131,c157]) ).
cnf(c159,plain,
truth = implies(X2,implies(not(X2),not(truth))),
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
implies(truth,implies(not(X2),not(truth))) = implies(implies(X2,implies(not(X2),not(truth))),implies(not(X2),not(truth))),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
implies(implies(X2,implies(not(X2),not(truth))),implies(not(X2),not(truth))) = implies(implies(implies(not(X2),not(truth)),X2),X2),
inference(substitution,[status(thm)],[c25]) ).
cnf(c162,plain,
implies(implies(implies(not(X2),not(truth)),X2),X2) = implies(truth,X2),
inference(congruence,[status(thm)],[c69]) ).
cnf(c163,plain,
implies(implies(implies(not(X2),not(truth)),X2),X2) = X2,
inference(transitivity,[status(thm)],[c162,c2]) ).
cnf(c164,plain,
implies(implies(X2,implies(not(X2),not(truth))),implies(not(X2),not(truth))) = X2,
inference(transitivity,[status(thm)],[c161,c163]) ).
cnf(c165,plain,
implies(truth,implies(not(X2),not(truth))) = X2,
inference(transitivity,[status(thm)],[c160,c164]) ).
cnf(c166,plain,
implies(not(X2),not(truth)) = X2,
inference(transitivity,[status(thm)],[c129,c165]) ).
cnf(c167,plain,
implies(not(not(X2)),not(truth)) = not(X2),
inference(substitution,[status(thm)],[c166]) ).
cnf(c168,plain,
implies(implies(not(not(X2)),not(truth)),not(truth)) = implies(not(X2),not(truth)),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
implies(implies(not(not(X2)),not(truth)),not(truth)) = X2,
inference(transitivity,[status(thm)],[c168,c166]) ).
cnf(c170,plain,
implies(implies(not(truth),not(not(X2))),not(not(X2))) = X2,
inference(transitivity,[status(thm)],[c127,c169]) ).
cnf(c171,plain,
implies(truth,not(not(X2))) = X2,
inference(transitivity,[status(thm)],[c125,c170]) ).
cnf(c172,plain,
not(not(X2)) = X2,
inference(transitivity,[status(thm)],[c4,c171]) ).
cnf(c173,plain,
not(not(x)) = x,
inference(substitution,[status(thm)],[c172]) ).
cnf(c174,plain,
$false,
inference(resolution,[status(thm)],[c1,c173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL140-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n018.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sun Sep 27 15:25:53 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.54 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.54
% 0.21/0.54 % SZS status Unsatisfiable
% 0.21/0.54
% 0.21/0.54 % SZS output start CNFRefutation
% See solution above
% 0.91/0.64
% 0.91/0.64 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------